CN112257027B - Power grid typical load day selection method based on normal distribution fitting - Google Patents
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Abstract
A method for selecting typical load day of a power grid based on normal distribution fitting comprises the steps of firstly using the frequency of load occurrence at the same moment of each day as the probability of load occurrence by using power grid load data. Because the load values at the same moment on different days are not much different, the load values are approximately considered to be compliant with normal distribution, then a curve of load and probability is fitted by using a moment estimation method, the curve is used as a probability density curve, and the expected value of each probability distribution is calculated as the load value at the moment. And finally, taking the absolute value of the difference between the daily load rate and the average daily load rate of the data as an evaluation index 1, taking the average value of the absolute values of the correlation coefficients of the selected typical load day and all the load days of the data as an evaluation index 2, and selecting the typical load day by the evaluation index 1 and the evaluation index 2.
Description
Technical Field
The invention relates to a method for selecting typical load days of a power grid.
Background
With the rapid development of domestic new energy, the problem of fossil energy deficiency in China is alleviated, but continuously increased new energy load peak-valley difference, intermittence and large fluctuation increase the phenomenon of reverse peak regulation of a power grid, and the predictability is reduced. The new energy is difficult to consume and connect with the network, and a large amount of wind and light abandoning phenomena are caused. In order to absorb a great amount of new energy, the support of an energy storage technology is needed, and when the energy storage is subjected to capacity configuration, peak-to-valley time division, load prediction, peak regulation and other works, a proper typical load day is needed to be selected.
At present, the typical load day is mainly selected by directly selecting the maximum peak-valley difference, the maximum load or the maximum load rate in quarters and the like, only a single index is considered, the whole factor is not considered, the selected typical load day is strong in pertinence row, the whole is not considered, and the selected typical load day is often not typical enough. Secondly, fuzzy clustering is performed on temperature or specific power grids through given indexes, the selected typical load day is a day which truly exists, and load data representing a quarter or a month may not be more accurate. The invention provides that the typical load day is selected through normal distribution fitting, and finally, the whole effect is considered by utilizing the fact that the typical load day selected is not actually existing.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a power grid typical load day selection method based on normal distribution fitting. According to the invention, the load data at the same moment is fitted by using normal distribution, and then the expected values at different moments are integrated into a new load day as a typical load day, so that the integral factors are comprehensively considered, and the utilization range of the selected typical load day is wider.
The technical scheme of the invention is as follows:
step 1, representing the probability of load occurrence by using the frequency of load occurrence at each moment;
the load occurrence probability is represented by the frequency of occurrence of the load at each time as follows:
wherein: p is p ij Represents the probability of load occurrence at the ith moment on the jth day, m ij The number of times of occurrence of the load at the ith moment in the whole data in the jth day is represented, n represents the total number of days contained in the data, j represents the number of days, and i represents the moment.
Step 2, fitting load data and the probability of load occurrence at each moment into a normal distribution curve by using a moment estimation method;
2.1 the normal distribution model is a probability distribution model commonly used in the engineering field, assuming that the variable X obeys a model with two parameters μ and σ 2 Is written as X is subjected to normal distribution N (μ, σ) 2 ) Then the probability density function f (x) of this normal distribution is:
to fit to a normal distribution, only μ and σ need to be determined 2 I.e., where μ is the expectation of a normal distribution, σ 2 For the variance of the normal distribution, p ij The probability of load occurrence at the i-th time on the j-th day is represented.
2.2 removing the repeated data obtained in step 1, and then adding the load value q at the i-th time on the j-th day ij Probability p of load occurrence at the ith moment in the jth day ij Respectively regarded as (x) 1j ，y 1j )，(x2 j ，y2 j )...(x ij ，y ij ) The subsequent calculation by using a moment estimation method is convenient, wherein q is as follows ij And x ij Indicating the load value at the i-th moment in the j-th day; p is p ij And y ij Representing the probability of load occurrence at the ith moment in the jth day; (q) ij ，p ij ) And (x) ij ，y ij ) In the coordinates representing the points, the abscissa is represented by the load value at the i-th time on the j-th day, and the ordinate is represented by the probability of occurrence of the load at the i-th time on the j-th day.
First x is ij J=1, 2,., n is taken as the total X at the i-th moment i The first-order origin moment and the second-order origin moment of the sample are shown in the formulas (3) and (4):
wherein E (X) i ) A first order origin moment which is the ith moment;a second order origin moment which is the i-th moment; d (X) i ) Is the variance of the ith moment; />Is the mean value of the ith moment; i=1, 2, 96; j=1, 2,. -%, n; x is x ij A load value indicating the j-th day at the i-th time; n represents the total number of days contained in the data, j represents the number of days, and i represents the time; 96 is the total number of time points of day;
let the mean and variance of normal distribution at the ith moment be mu i And theta i Then its moment estimate is:
in the method, in the process of the invention,and->Respectively estimating the mean value and the variance of normal distribution at the ith moment; />Is the mean value of normal distribution at the ith moment; i=1, 2, 96; j=1, 2,. -%, n; x is x ij A load value indicating the j-th day at the i-th time; n represents the total number of days contained in the data, j represents the number of days, and i represents the time; 96 is the total number of time points of day.
And step 3, obtaining mathematical expectation of the load probability distribution at each moment, and taking the expectation value as the load value at the moment.
Obtaining a load probability distribution function at each moment through moment estimation, and obtaining the expected distribution through a formula (6):
E(x i )＝∫x i f(xi)dx i (6)
wherein E (x) i ) Indicating the desire at the i-th time; x is x i An argument representing a normal distribution function at the i-th time; f (x) i ) Representing the ith moment argument x i Probability density function of (a).
This expected value E (x i ) As the load value at this time, after the load values are obtained by the above steps for 96 times of day, a new load value of one day is composed of the 96 load values, and the load data of the new day is used as the selected typical load day data, i.e., E (x) 1 )，E(x 2 )，...E(x 96 )。
And 4, synthesizing the load data obtained in the step 3 into a typical load day, and then calculating an absolute value of a difference between the daily load rate and the average daily load rate of the data as an index 1 and an average value of correlation coefficient absolute values of the typical load day and all the load days as an index 2.
The daily load rate is the ratio of daily average load to daily maximum load, and is used to describe a daily load curve, and represents the imbalance of load distribution in one day, namely:
wherein, gamma j Represents the daily load rate on day j, q ij The load value at the ith moment in the jth day; 96 represents the total number of times of day.
The calculation method of index 1 is as follows:
wherein z is 1 Indicating index 1; gamma ray d Representing the load rate of the selected typical load day; n represents the total number of days of the load data, and J represents a certain day.
Index 1 reflects the difference between the daily load rate of the selected representative load day and the average level of data, and the smaller the value, the more representative the representative load day is selected.
4.2 pearson correlation coefficient can describe the correlation of two sets of data well, set to have two sets of X, Y, when r >0 and the coefficient is bigger, the positive correlation of the two sets of data is stronger, when r <0 and the coefficient is smaller, the negative correlation of the two sets of data is stronger. The correlation coefficient r is:
wherein r represents a correlation coefficient, and x= { X 1 ，x 2 ，...，x n }，Y＝{y 1 ，y，...，y n Two arrays, n representing the number of elements in the array, gamma j Represents the daily load rate on day j, x i An argument representing a normal distribution function at the i-th moment,represents the mean value of array X, +.>Representing the average value of array Y.
Since the larger the absolute value of the correlation coefficient is, the stronger the correlation is, and then the average value of the absolute values of the correlation coefficients of the typical load day and all the load days of the data is taken as an index 2, and the calculation method of the index 2 is as follows:
wherein z is 2 Representing index 2, r j The correlation coefficient of the typical load day with the j-th day is shown, and n represents the number of days of the data used.
The larger index 2 indicates that the more load-dependent the selected representative load day is with the other days, the better the selected representative load day is.
Drawings
FIG. 1 is a flow chart of a typical load day selection method of the present invention implemented based on normal distribution fitting.
Detailed Description
The invention is further described below with reference to the drawings and detailed description.
As shown in fig. 1, the typical load day selection method based on normal distribution fitting of the present invention has the following flow:
1. the frequency of occurrence of the load data at the same moment on different days is calculated, the probability is expressed by the frequency, and the probability of occurrence of the load at each moment is obtained, wherein the calculation method is shown in a formula (1).
2. And fitting the load data at each moment and the probability of occurrence into a normal distribution curve by using a moment estimation method.
The normal distribution model is a probability distribution model which is frequently used in the engineering field, and the formula (2) is a normal distribution model. And removing repeated data in the load at the same moment, substituting the load and the occurrence probability thereof into the formula (2) by using a moment estimation method, and then obtaining normal distribution basic parameters by using the formulas (3), (4) and (5).
3. The mathematical expectation of the load probability distribution at each moment is obtained, and the expectation value is taken as the load value at the moment.
The probability distribution function of the load at each moment is obtained through moment estimation, the probability distribution function is carried into a formula (6) to find the expectation, and the expectation is taken as the load value at the moment.
4. The resulting load data was synthesized as a typical load day and then index 1 was calculated: absolute value of difference between daily load rate and data average daily load rate and index 2: average of absolute values of correlation coefficients of typical load day and data all load days.
The daily load rate is the ratio of the daily average load to the daily maximum load, and is used for describing a daily load curve and representing the unbalance of the load distribution in one day, the daily load rate is calculated by the formula (7), and then the index 1 is calculated by the formula (8). Index 1 reflects the difference between the daily load rate of the selected representative load day and the average level of data, and the smaller the value, the more representative the representative load day is selected.
The pearson correlation coefficient can well describe the correlation of two groups of data, and two groups of X and Y are arranged, when r >0 and the coefficient is larger, the positive correlation of the two groups of data is stronger, and when r <0 and the coefficient is smaller, the negative correlation of the two groups of data is stronger. The correlation coefficient r can be calculated by equation (9), and then index 2 is calculated by equation (10). The larger index 2 indicates that the more load-dependent the selected representative load day is with the other days, the better the selected representative load day is.
Claims (4)
1. A power grid typical load day selection method based on normal distribution fitting is characterized by comprising the following steps:
step 1, representing the probability of load occurrence by using the frequency of load occurrence at each moment;
step 2, fitting the load data and the load occurrence probability at each moment into a normal distribution curve by using a moment estimation method;
in the step 2, the method for fitting the load data and the load occurrence probability at each moment into a normal distribution curve by using a moment estimation method is as follows:
probability density function f (x) according to normal distribution:
wherein μ is the expectation of normal distribution, σ 2 For normal distribution variance, the variable X obeys a set of two parameters μ and σ 2 Is written as X is subjected to normal distribution N (μ, σ) 2 )；
Removing the repeated data obtained in the step 1, and adding the load value q at the ith moment in the jth day ij Probability p of load occurrence at the ith moment in the jth day ij Respectively regarded as (x) 1j ，y 1j )，(x 2j ，y 2j )…(x ij ，y ij ) Wherein x is ij Indicating the load value at the i-th moment in the j-th day; y is ij Representing the probability of load occurrence at the ith moment in the jth day; (q) ij ，p ij ) And (x) ij ，y ij ) Coordinates representing points wherein the abscissa is represented by the i-th moment load value on the j-th day and the ordinate is represented by the probability of occurrence of the i-th moment load on the j-th day;
first x is ij (j=1, 2,., n) as the i-th moment overall X i The first-order origin moment and the second-order origin moment of the sample are shown in the formulas (3) and (4):
wherein E (X) i ) A first order origin moment which is the ith moment;a second order origin moment which is the i-th moment; d (X) i ) Is the variance of the ith moment; />Is the mean value of the ith moment; i=1, 2, 96; j=1, 2,. -%, n; x is x ij A load value indicating the j-th day at the i-th time; n represents the total number of days contained in the data, j represents the number of days, and i represents the time; 96 is the total number of time points of day;
let the mean and variance of the i-th moment distribution be μ respectively i And theta i Then its moment estimate is:
in the method, in the process of the invention,and->Respectively estimating the mean value and the variance of normal distribution at the ith moment; />Is the mean value of normal distribution at the ith moment; i=1, 2, 96; j=1, 2,. -%, n; x is x ij A load value indicating the j-th day at the i-th time; n represents the total number of days contained in the data, j represents the number of days, and i represents the time; 96 is the total number of time points of day;
step 3, calculating mathematical expectation of load probability distribution at each moment, and taking the expectation value as a load value at the moment;
step 4, synthesizing the obtained load data into typical load days, and then calculating an index 1: absolute value of the difference between the daily load rate and the data average daily load rate, and index 2: average of absolute values of correlation coefficients of typical load day and data all load days.
2. The method for selecting a representative load day according to claim 1, wherein the method for calculating the frequency of occurrence of the load is as follows:
wherein: p is p ij Represents the probability of load occurrence at the ith moment on the jth day, m ij The number of times the load at the ith moment appears at the ith moment in the whole data in the jth day is represented, and n represents the total number of days in which the data is contained.
3. The method for selecting a typical load day according to claim 1, wherein the method for selecting a typical load day in step 3 comprises the following steps:
obtaining a load probability distribution function at each moment through moment estimation, and obtaining the expected load probability distribution through a formula (6):
E(x i )＝∫x i f(x i )dx i (6)
wherein E (x) i ) Indicating the expected value at the i-th time; x is x i An argument representing a normal distribution function at the i-th time; f (x) i ) Representing the ith moment argument x i Probability density functions of (2);
taking the expected value as the load value of the moment, obtaining the load values of 96 moments of a day according to the steps, forming a new load value of a day by the 96 load values, and taking the load data of the new day as the selected typical load day data, namely E (x) 1 )，E(x 2 )，...E(x 96 )。
4. The method according to claim 1, wherein the index of the representative load day selected in the step 4 is calculated as follows:
daily load rate is the ratio of daily average load to daily maximum load, and is used to describe daily load curves, which characterize the imbalance of load distribution in a day, namely:
wherein, gamma j Represents the daily load rate on day j, q ij The load value at the ith moment in the jth day;
the calculation method of the index 1 is as follows:
wherein z is 1 Indicating index 1, gamma d Load rate of representative load day selected, n represents days of data used;
describing the correlation of two groups of data by using the pearson correlation coefficient, and setting two groups of X and Y, wherein when r is larger than 0 and the coefficient is larger, the positive correlation of the two groups of data is stronger, and when r is smaller than 0 and the coefficient is smaller, the negative correlation of the two groups of data is stronger, and the correlation coefficient r is:
wherein r represents a correlation coefficient, and x= { X 1 ，x 2 ，...，x n }，Y＝(y 1 ，y，...，y n Two arrays, n representing the number of elements in the array, gamma j Represents the daily load rate on day j, x i An argument representing a normal distribution function at the i-th moment,represents the mean value of array X, +.>Representing the average value of the array Y;
the average value of the absolute values of the correlation coefficients of the typical load day and the data on all load days is taken as an index 2, and the index 2 is calculated as follows:
wherein z is 2 Representing index 2, r j A correlation coefficient representing a typical load day and a j-th day, and n represents the number of days of data used;
the larger index 2 indicates that the more load-dependent the selected representative load day is with the other days, the better the selected representative load day is.
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